Supernovae with JWST

Detection and classification of supernovae beyond redshift with the James Webb Space Telescope

Abstract

Future time-domain surveys for transient events in the near- and mid-infrared bands will significantly extend our understanding about the physics of the early Universe. In this paper we study the implications of a deep ( mag), long-term ( years), observationally inexpensive survey with the James Webb Space Telescope (JWST) within its Continuous Viewing Zone, aimed at discovering luminous supernovae beyond redshift. We explore the possibilities for detecting Superluminous Supernovae (SLSNe) as well as Type Ia supernovae at such high redshifts and estimate their expected numbers within a relatively small ( deg) survey area. It is found that we can expect new SLSNe and SNe Ia discovered in the redshift range. We show that it is possible to get relatively accurate () photometric redshifts for Type Ia SNe by fitting their Spectral Energy Distributions (SED), redshifted into the observed near-IR bands, with SN templates. We propose that Type Ia SNe occupy a relatively narrow range on the JWST F220W-F440W vs F150W-F356W color-color diagram between rest-frame days around maximum light, which could be a useful classification tool for such type of transients. We also study the possibility of extending the Hubble-diagram of Type Ia SNe beyond redshift 2 up to . Such high- SNe Ia may provide new observational constraints for their progenitors as well as the cosmic star formation rate.

cosmology: cosmological parameters — cosmology: distance scale — cosmology: early universe — galaxies: stellar content — stars: supernovae: general
1\correspondingauthor

Jozsef Vinko

0000-0002-9498-4957]Enikő Regős

0000-0001-8764-7832]József Vinkó

1 Introduction

One of the fundamental questions of modern astrophysics and cosmology is related to the problem of star formation in the early Universe: how did the Universe make its first stars? Decade-long observational and theoretical efforts have been devoted to reveal and establish the cosmic Star Formation Rate (SFR) as a function of redshift (see e.g. Hopkins & Beacom, 2006; Behroozi, Wechsler & Conroy, 2013; Madau & Dickinson, 2014; Bouwens et al., 2014; Oesch et al., 2015, and references therein). This function gives the mass of newborn stars per year per volume element, and it is a strong function of the cosmic time, i.e. redshift, up to (Oesch et al., 2018).

One of the exciting possibilities to probe the cosmic SFR at various redshifts is the discovery of new transients that are related to the death of massive stars, i.e. long-duration gamma-ray bursts (LGRBs) and supernovae (SNe). LGRBs are now routinely detected at redshifts beyond , but it is still very challenging observationally for SNe. Because the upcoming near- and mid-infrared surveys offer new opportunities for such efforts (e.g. Tanaka et al., 2013), Wang et al. (2017) proposed the First Lights At REionization (FLARE) project for discovering various types of transients with NASA’s James Webb Space Telescope (JWST) at the highest possible redshifts. One of the most important (and most ambitious) goals of the FLARE project is the discovery of the most distant, most luminous supernovae with JWST.

Superluminous supernovae (SLSNe), which have the highest intrinsic peak luminosities among SNe known to date, seem to be promising targets for such a purpose, because they can be potentially detected up to redshifts with deep surveys (Tanaka et al., 2013). As they are produced by very massive progenitors, they can closely trace the cosmic star formation rate variation along redshift. Thus, discovering SLSNe at very high redshifts can provide unprecedented information on the history of early star formation and evolution.

Thermonuclear (Type Ia) SNe offer another possibility to shed light on star forming processes in the early Universe. Type Ia SNe are fainter, but more abundant (at least in the local Universe) than SLSNe. They have absolute AB magnitude at peak, and relatively UV-faint SED at and after maximum light. They are produced by exploding white dwarfs (WDs): either a single mass-gaining WD near the Chandrasekhar limit (single degenerate channel, SD) or two merging WDs (double-degenerate channel, DD) (Maoz et al., 2014; Livio & Mazzali, 2018).

Because WDs are formed from low-mass ( M) stars at the end of their lifetime, a delay between the birth of a new star and the explosion of the WD is expected (e.g. Graur et al., 2014; Maoz et al., 2014). The delay-time distribution (DTD) depends on the progenitor channel, i.e. the SD and DD scenarios. A “prompt” channel that contains SNe Ia that explode very shortly ( Myr) after the formation of the WD were examined by Scannapieco & Bildsten (e.g. 2005); Raskin et al. (e.g. 2009). The existence of such a “prompt” Ia population can be critically probed with detections of high- SNe Ia (Regős, 2013; Rodney et al., 2014). Furthermore, direct measurements of the SN Ia DTD may help in distinguishing between the SD and DD scenarios. It is possible that both channels operate, either on short (SD) or long (DD) time scales. For example, the combined data from the CLASH and CANDELS surveys are consistent with long delay times corresponding to the DD scenario (Rodney et al., 2014).

In this paper we focus on one particular topic within the FLARE project: observing the most distant, most luminous supernovae with JWST. We explore the feasibility of detecting and classifying different types of SNe, thermonuclear (Type Ia SNe) and superluminous supernovae (SLSNe) in particular, beyond with JWST, as well as measuring their physical properties from spectrophotometry and extending the observed Hubble-diagram for SNe Ia at as high redshifts as possible.

High-redshift Type Ia SNe are used to derive cosmological parameters from their Hubble-diagram (see e.g. Scolnic et al., 2018, and references therein). With the help of SNe it is possible to extend the Hubble diagram to , testing the constancy of dark energy with time and probing progenitor evolution. To study the properties of dark energy one measures its equation of state and time variation to distinguish among cosmological explanations. Departure from or detection of would indicate a present epoch of weak inflation. Detecting SNe Ia at provides the unique chance to test SN Ia distance measurements for the deleterious effects of evolution independent of our ignorance of dark energy. We can also test DD and SD scenarios by measuring the SNe Ia delay time distribution. The CLASH (Postman et al., 2012) and CANDELS (Koekemoer et al., 2011; Grogin et al., 2011) programs provided measurement of the SN Ia rate up to , and FLARE, as planned, will be capable of going beyond 2.

2 Survey strategy for high-redshift transients using Jwst

Recently Tanaka et al. (2013) showed that a moderately deep ( mag) deg survey in the near-infrared (NIR) can potentially discover SLSNe up to redshift . With a mag deeper limiting magnitude the redshift limit could be pushed even further, toward .

Because such kind of a survey is observationally very expensive with JWST, Wang et al. (2017) proposed another observing strategy for discovering high-redshift SNe: continuous monitoring of a smaller area toward the North Ecliptic Pole with JWST.

The JWST North Ecliptic Pole (NEP) Time-Domain Field (TDF) is a sq. degree area within the JWST northern Continuous Viewing Zone (Jansen & Webb Medium Deep Fields IDS GTO Team, 2017). The FLARE project intends to take deep AB mag) observations with JWST Near Infrared Camera (NIRCam) for at least three years, utilizing the F150W (), F200W (), F356W () and F444W () filters. Mapping the TDF with NIRcam will be repeated with a days cadence in the observer’s frame in order to find (and follow-up, if possible) transients.

The proposed series of observations would map a field-of-view (FoV) of arcmin (0.083 deg) area down to at least AB-magnitude in all four NIRCam filters. More technical details on the proposed observations can be found in Wang et al. (2017).

In the following we use these basic observational constraints to simulate photometric data for a sample of SNe taken with the four JWST NIRCam filters listed above. We evaluate the number of potentially detectable SNe, and explore the possibilities for estimating their redshifts as well as extending the Hubble-diagram for Type Ia SNe toward – 6. A similar study on the planned WFIRST Supernova Survey can be found in Hounsell et al. (2017).

3 Star formation at high redshifts

The first natural question that needs to be answered is the number of SNe detectable at redshifts beyond . In order to predict this number one must know the cosmic star formation rate (SFR) at such high redshifts.

To date numerous forms of parametrized functions have been proposed to represent the redshift dependence of the cosmic SFR (see e.g. the references given in Section 1). In the following we adopt and use the parametrization given by Hopkins & Beacom (2006):

(1)

where , and , , , are assumed following Hopkins & Beacom (2006). Because we primarily focus on supernova rates, the factor is constrained by scaling the theoretical SN rates derived from the SFR to the observed SN rates (see below).

Since Eq. 1 is determined from data, it can be extrapolated safely only up to . Between we use the observational constraints given by Oesch et al. (2015) based on the UV luminosity function of high-redshift galaxies observed with the Hubble Space Telescope (HST). The redshift dependence of the SFR in this interval is

(2)

which is scaled to match the Eq. 1 at . Eq. 2 represents the upper limit of the observed high- SFR above (Oesch et al., 2015). For the lower limit at we adopted

(3)
Figure 1: Parametrized forms of the cosmic SFR as a function of redshift. The Hopkins & Beacom (2006) form plus the extension based on Oesch et al. (2015) is adopted for further calculations, but the other forms would have given very similar results.

Several other forms of the high-redshift SFR are available over . For example, Madau & Dickinson (2014) proposed

(4)

while Behroozi, Wechsler & Conroy (2013) obtained

(5)

with , , and in the unit of Eq. 4.

All of these functions give very similar redshift dependence of the cosmic SFR, as illustrated in Fig. 1. They predict a peak around -3 and a declining trend toward both lower and higher redshifts.

4 Supernovae at high redshifts

In this section we explore the detectability of the two brightest classes of supernovae, namely SLSNe and Type Ia SNe beyond with JWST NIRCam. We use model Spectral Energy Distributions (SEDs) for these SN types close to maximum light to predict the observed fluxes for redshifted SNe in the bandpasses covered by the NIRCam filters.

4.1 Superluminous Supernovae

SLSNe are the brightest SNe known to date; they can reach or outshine mag in any wavelength bands in the optical or near-ultraviolet (Quimby et al., 2011; Gal-Yam, 2012). Observationally they can be classified into two, maybe three subclasses: members of the SLSN-I class do not show hydrogen in their spectra, unlike the hydrogen-rich SLSN-II events (note that in recent literature the hydrogen-poor SLSN-I events are often referred to simply as SLSNe, which might be a source of potential confusion, because the statistical properties of the two subclasses are systematically different, see below). There might be a third, very rare class, named SLSN-R, that also contains hydrogen-poor objects whose slowly evolving light curves are thought to be powered by extreme amount ( M) of radioactive Ni (Gal-Yam, 2012). Such extreme amount of Ni could be produced in a very massive core-collapse event induced by pair instability (e.g. SN 2007bi, Gal-Yam et al., 2009). The powering mechanism of the first two subtypes is still debated: several models including magnetar spin-down (e.g. Kasen & Bildsten, 2010; Nicholl et al., 2017), or interaction with hydrogen-poor circumstellar shell (Chatzopoulos et al., 2012, 2013) have been proposed, but none of them are able to fully explain all observational aspects of SLSNe.

SLSN-I events are usually found in low-mass, metal-poor host galaxies that most often show extremely strong emission features (Neill et al., 2011; Lunnan et al., 2014; Leloudas et al., 2015; Perley et al., 2016). In this respect SLSNe-I are similar to LGRBs that also tend to prefer low metallicity hosts (e.g. Langer & Norman, 2006; Woosley & Bloom, 2006; Perley et al., 2016). SLSNe-II, however, do not seem to show this trend: they can appear in galaxies that have broader range of mass and metallicity (Perley et al., 2016).

Figure 2 shows the blackbody-fitted SEDs of SLSNe at peak brightness shifted to various redshifts. These SEDs were constructed by combining observed, flux-calibrated spectra of various SLSNe (see Wang et al., 2017, for details). It is seen that both SLSN-I and SLSN-II events, in principle, are expected to be brighter than the NIRCam detection limit in the FLARE survey ( AB-mag) up to , in good agreement with the results by Tanaka et al. (2013). Based on this prediction, in Section 5 we estimate the expected number of SLSNe during the FLARE survey time.

Figure 2: Modeled SEDs of SLSNe-I (left panel) and II (right panel) at different redshifts.

4.2 Thermonuclear Supernovae (Type Ia SNe)

The left panel in Figure 3 shows the observable peak AB-magnitudes of SNe Ia with the four JWST NIRCam filters as above plus two broadband NIRCam W2 filters centered at and microns. These curves were calculated from synthetic photometry using the above mentioned JWST filter bandpasses on the Hsiao-templates for Type Ia SNe (Hsiao et al., 2007). It is seen that SNe Ia are expected to reach the FLARE detection limit in several NIRCam bands up to . The right panel of Fig.3 illustrates the same conclusion by showing the blackbody-fitted SEDs of SNe Ia (Wang et al., 2017) at various redshifts. Thus, detections of SNe Ia with JWST NIRCam is feasible in the redshift range of .

Figure 3: Left panel: Peak magnitudes of Ia SNe in the NIRCAM passbands as a function of redshift. Right panel: Model SEDs of SNe Ia at different redshifts.

5 The volumetric SN rate at high redshifts

For the rest of this paper we adopt the standard -CDM cosmology with the following parameters: (Planck collaboration, 2014), defined as Planck13 in astropy.cosmology (Astropy Collaboration, 2013).

For the cosmic star formation rate we apply the form defined by Hopkins & Beacom (2006) (Equation 1) with the extension between as in Equation 2 and for as in Equation 3 (Oesch et al., 2015) (see Section 3 for details).

5.1 SLSNe

Figure 4: Left panel: Assumed volumetric rates of SLSNe-I and II as a function of redshift. Right panel: the predicted number of SLSNe in the survey field at different redshifts during the proposed 3-year-long survey.
Redshift N(I)2 N(I)3 N(II)4 N(II)5
0.5 0 0 0 1
1.5 0 1 2 5
2.5 0 2 2 8
3.5 0 1 1 6
4.5 0 1 0 3
5.5 0 0 0 1
Table 1: The expected numbers of SLSN-I and II events during the survey.

Since SLSNe are thought to originate from very massive stars, there is practically no delay time between the formation of their progenitors and the explosion. However, the local (low-) observed rates for SLSNe-I are probably biased by the fact that they tend to occur only in low-metallicity hosts, similar to LGRBs (Section 4.1). Because at high redshifts low-metallicity host galaxies are more abundant, the SLSN-I rates at are expected to be boosted up with respect to a rate that is estimated simply by extrapolating the local observed rate with the function. Thus, the observed SLSN rate per redshift bin can be expressed as

(6)

where is the comoving volume,

(7)

is the comoving rate of SLSNe, is the cosmic star formation rate, and is the redshift-dependent efficiency factor that corrects for the metallicity dependence. For SNe with negligible metallicity dependence (e.g. SLSN-II), .

The effect of metallicity on the rates of high-redshift GRBs has been extensively studied in the literature. For example, using model grids of single star progenitors of LGRBs, Yoon et al. (2006) computed the redshift-dependent GRB rate by using metallicity-dependent SFR and adding binaries to the collapsar model of the LGRB progenitors. From the metallicity-dependent star formation history, the observed mass function and the mass – metallicity relation they computed the expected GRB rate as function of metallicity and redshift. More recently, many studies found that the metallicity dependence can be parametrized simply by multiplying the function with the efficiency factor , where (Kistler et al., 2009; Virgili et al., 2011; Robertson & Ellis, 2012; Trenti et al., 2013).

Based on the rate modelling of GRBs by Trenti et al. (2013), Wang et al. (2017) applied the DRAGONS semi-analytic galaxy formation model (Mutch et al., 2016) to estimate the expected number of SLSNe at high redshifts. As the progenitor models are poorly constrained, they considered simple empirically motivated models using the mean stellar metallicity of every galaxy at each simulated redshift to calculate the SLSN production efficiency factor, using stellar evolution simulations similar to Yoon et al. (2006) for each galaxy and average over all galaxies at that redshift. Assuming strong metallicity dependence they obtained a metallicity correction for the SLSN rate that is similar to that of the GRBs found previously (see above). In particular, they found that the peak of the SLSN rate shifts significantly toward if strong metallicity dependence is assumed with respect to the peak at when no metal dependence is used.

Recently Prajs et al. (2017) calculated the volumetric rate of SLSNe at . They also estimated the rate of ultra-long GRBs based on the events discovered by the Neil Gehrels Swift satellite, and showed that it is comparable to the SLSN rate, providing further evidence of a possible connection between these two classes of events.

As the studies mentioned above explain the observed redshift evolution of the ratio of GRB rates and SFR as (with some increment from the power law at high redshift), we use this redshift dependence for in Equation 7, i.e. . As the metallicities average out through the mass function at a given redshift, this factor provides a reasonable correction for the redshift-dependence of the frequency in low- and high-metallicity host galaxies.

For SLSNe-I we use the observed local volumetric rates published by Cooke et al. (2012), Quimby et al. (2013) and Prajs et al. (2017). For SLSNe-II we adopt the observational rate as given in Quimby et al. (2013), which recently turned out to be consistent with the rates estimated from three SLSNe discovered at (Moriya et al., 2018). Since the metallicity dependence of SLSN-II events is less pronounced as for SLSNe-I, their rates at high redshifts might be closer to the one that can be obtained by simply extrapolating their local rates toward higher redshifts along with the function. Nevertheless, we also apply the same redshift dependent metallicity correction as above for SLSNe-II as well in order to get an upper limit for their high- rates.

The expected number of SLSNe between redshifts and can be calculated by integrating Equation 7 to get

(8)

where is the survey area and is the survey time. The results (the number of SNe per unit redshift interval within the survey area during the total survey time) are shown in Table 1, where the columns list the predicted number of SLSN-I and II events with and without the metallicity correction.

The left panel of 4 displays the adopted SLSNe volumetric rates as a function of redshift. The right panel shows the predicted numbers of SLSNe in the survey field at different redshifts with and without the assumed redshift-dependent metallicity correction. It is seen that even if we continue the survey up to 3 years in the observer’s frame, we can expect only very few SLSNe-I at relatively low (-3) redshifts. SLSNe-II look to be more abundant than SLSNe-I, thus, it is more probable that the newly discovered high- SLSNe will be SLSN-II events, especially if their rate also (at least slightly) depends on the host metallicity. On the other hand, even though SLSNe can be potentially detectable with JWST up to , their very low volumetric rate make them less suitable for constraining the cosmic SFR at , at least with the relatively small-area survey considered in this paper.

5.2 Type Ia SNe

The volumetric rate for Type Ia SNe is different from that of core collapse events. Since the progenitors of Type Ia SNe are binaries containing at least one white dwarf (i.e. evolved) star, a significant delay time between their formation and the SN explosion is expected. Therefore, their rate can be expressed as

(9)

where the efficiency is the number of SNe formed per unit stellar mass (), that is the fraction of white dwarfs in the 3-8 range, is the formation redshift and is their delay time distribution.

In the SD scenario (corresponding to short delay times), from simple analytic modelling of main-sequence lifetime as a function of mass (e.g. Barbary, 2011) one can get

(10)

On the other hand, double degenerates (long delay) result in

(11)

Population synthesis models predict universal DTD shapes for SNe Ia, independent of the details of common envelope prescription, mass transfer rate, hydrogen retention efficiency or metallicities (Nelemans et al., 2013; Moe & Di Stefano, 2013). For example, Strolger et al. (2004) considered two general forms for the DTD to explain the redshift distribution of SNe Ia discovered in the Hubble Higher-z Supernova Search program between . They applied exponential distributions like

(12)

or Gaussian distributions

(13)

assuming either wide () or narrow () Full Width at Half Maximum (FWHM) for the latter. Also, the peak of the Gaussian distributions were set in between Gyr. Strolger et al. (2004) found Gyr as their best-fit value.

Although at present most of the observational evidence point toward the DTD (e.g. Maoz et al., 2014), in this paper we consider all the DTD forms mentioned above to predict the expected redshift distribution of SNe Ia at redshifts. For the delay-time parameter we assume = 0.5, 1.0, 2.0, 3.0 and 4.0 Gyr.

In Figure 5 the top left panel shows the observed SN Ia rates (black circles) collected from literature (Graur et al., 2011, and references therein) as well as various theoretical rates corresponding to different DTD forms listed above. Also shown is the SN Ia rate applied by Hounsell et al. (2017) for estimating the number of SNe Ia in the WFIRST Supernova Survey:

(14)

It is seen that the known observed rates are not constraining the various DTD scenarios in the range. The new SN Ia discoveries beyond would therefore provide critical and unprecedented information on the real DTD as well as on the cosmic SFR at high redshifts.

The other panels in Figure 5 plot the expected numbers of SNe Ia in the arcmin survey field during the total survey time (3 years) assuming the various DTD functions detailed above. All numbers are normalized to the same value in the first redshift bin centered at . Black circles show the no-DTD case (i.e. if all SNe Ia were prompt explosions, like core-collapse SNe), which serves as an upper limit for higher redshifts. It is seen that the various DTDs predict significantly less number of SNe Ia at than the no-DTD scenario, as expected, but their redshift distributions are more or less similar to each other, except maybe the Gauss-narrow DTD (bottom left panel). Table 2 lists these numbers for the SD, DD and no-DTD cases.

Figure 5: Top left panel: The observed SN Ia rates as a function of redshift (open circles) compared to the rates assumed in Hounsell et al. (2017) (brown curve), and the ones calculated with different forms of DTD (see text). The assumed SFR (Oesch et al., 2015) corresponding to negligible DTD is also shown as a dotted curve. Top right panel: the expected number of SNe during the survey time (3 years) assuming no DTD (black circles), and various forms of DTD (colored lines and symbols) as indicated in the legend. All curves are normalized to the same value at . Bottom left panel: the same as the top right panel, but with the Gauss-narrow DTD. Bottom right: the same as the top right panel, but with the Gauss-wide DTD.
Redshift N(Ia) N(Ia) N(Ia)
(SD) (DD) (no DTD)
0.5 14 14 14
1.0 28 33 43
1.5 32 41 65
2.0 29 40 74
2.5 22 33 70
3.0 15 23 54
3.5 9 15 36
4.0 6 9 22
4.5 3 5 13
5.0 2 3 7
Table 2: The expected numbers of SNe Ia in the survey field.

6 SN Ia simulations

In this Section we aim at extending the Hubble-diagram for Type Ia SNe beyond redshift . In order to discover, classify and analyze a statistically significant sample of Type Ia SNe with JWST, a robust methodology for all of these tasks is needed. In this Section we use a simulated sample of Ia SNe computed by applying the sncosmo6 code (Barbary et al., 2016) that is designed to simulate SEDs and light curves of Type Ia SNe at any redshift.

We simulate a 3 year-long photometric survey of SNe Ia by generating a sample of 434 SNe distributed in redshift interval between and 7 according to the SN Ia volumetric rate discussed in Section 5. In order to get a relatively high number of SNe, the no-DTD scenario is assumed, i.e. the distribution of SNe in redshift simply followed the cosmic SFR. Thus, the number of high- SNe are probably overestimated in this simulation, and may not represent the true expected number of SNe Ia to be discovered with JWST, but this simulated sample is better suitable for computing statistics.

The epoch of maximum light for each SN is distributed uniformly within the 3 year-long survey window (in the observer’s frame), and observational epochs with a regular cadence of 90 days are set during the survey time. This resulted in a maximum of 12 observational epochs in this simulation.

Luminosity distances are assigned to the simulated SNe via the astropy.cosmology module by adopting the Planck13 cosmology model, as above. To model the SED of the simulated SNe as a function of time we use the Hsiao templates (Hsiao et al., 2007). It is known that these templates do not capture the peak brightness - decline rate - color dependence (i.e. the Phillips-relation), unlike the SALT2 templates (Guy et al., 2007). However, the Hsiao templates extend up to 2.5 microns in rest-frame wavelengths, while the SALT2 templates are defined only between 0.35 and 0.7 microns. Thus, in principle, the Hsiao templates allow the computation of synthetic photometry in all 4 JWST NIRCam bands simultaneously for redshifts .

The distribution of the peak absolute brightnesses of the simulated SNe are approximated by assuming that their rest-frame V-band magnitudes have Gaussian distribution around the mean value of mag and a FWHM of mag (Richardson et al., 2014). Such a distribution may predict a few SNe Ia brighter than mag at peak, which are not frequently observed, but could be associated with the brightest 91T/Super-Chandra Ia events (e.g. 2007if, Yuan et al., 2010).

Having the redshift (), luminosity distance (), moment of maximum light () and rest-frame V-band absolute magnitude ((max)) for each simulated SN, we compute synthetic photometry in the JWST NIRCam F150W, F200W, F356W and F444W filter bandpasses at each observational epoch by taking into account time dilation and flux density corrections due to redshift. Dust extinction within the host galaxy is ignored as a first approximation, while dust extinction in the Milky Way should be negligible in these JWST bandpasses. Ignoring the dust extinction in the host galaxies certainly makes our results somewhat more optimistic than the reality, but reduces the dependency on the assumed dust distribution priors. Nevertheless, these simulations are still useful to reveal the most obvious properties and limitations of the proposed FLARE survey.

6.1 Statistics

Figure 6: Left panel: the histogram of the rest-frame V-band absolute magnitudes of the simulated SNe. Right panel: the redshift distribution of the simulated SNe.

In the left panel of Figure 6 the histogram of the V-band absolute peak brightnesses for the simulated SNe is plotted, while the right panel shows the distribution of the same SN sample in redshift space. The distribution of peak brightnesses introduces a large scatter in the observed peak magnitudes on the Hubble diagram. This scatter can be reduced by applying the ’stretch’- or ’decline-rate’ correction which is commonly applied for SNe Ia when light curves in the rest-frame optical bands are available. However, in the proposed FLARE survey, as shown below, well-sampled light curves cannot be expected. Thus, alternative methods for taking into account and correcting for the peak brightness distribution are needed.

We define two types of detection in our simulation. “Strong detection” means that a particular SN is detected (i.e. brighter than 27.3 AB-magnitude, see Section 2) in all 4 NIRCam filters simultaneously at a given epoch. “Weak detection” is defined as a detection only in at least one NIRCam bandpass at a given epoch. In the full sample containing 434 simulated SNe, 87 pass the “strong detection” criterion on at least 1 epoch during the survey, but only 9 of them are detected on 2 epochs. The maximum redshift of these SNe turned out to be , while the average redshift of the “strong detection” subsample is . The number of SNe in the “weak detection” group is 361, 102 of which are detected on 2 epochs. The maximum redshift in the “weakly detected” sample was 6.77, while the mean redshift of this subsample is .

These numbers suggest that even though a significant number () of SN Ia detections in all 4 JWST NIRCam filter bands is expected during the proposed 3 year-long survey, only % of them would be detected on 2 consecutive epochs. Such a sparsely sampled “light curve” is clearly not capable of providing the necessary correction for the peak brightness distribution via the usual stretch/decline rate measurement. Moreover, since conventional spectroscopic observations are not feasible for SNe at , the determination of the redshifts of the detected SNe must rely solely on photometry.

In the following sections we explore the possibilities and the feasibility of estimating the redshift and the true peak brightness of SNe from JWST NIRCam photometry.

6.2 Estimating photometric redshifts

Figure 7: Examples of “observed” SEDs (filled symbols) and synthetic magnitudes derived from the best-fit Hsiao-models (lines).
Figure 8: Photometric redshifts of simulated SNe Ia derived by fitting Hsiao-templates to fluxes in 4 NIRCAM filter bandpasses. See text for details.

As shown in the previous section, the redshifts of SNe detected with JWST in the FLARE survey must be determined from photometric/SED data. Having accurate and precise photometric redshifts may enable the use of SNe Ia, measured only with photometry, to probe cosmology. This can dramatically increase the science return of future supernova surveys.

For example, the Large Synoptic Survey Telescope will use improved versions of the analytic photo-z estimator of Wang (2007) and Wang et al. (2007). That method uses colors as well as peak magnitudes, or colors only, to estimate the redshift of SNe Ia. It is an empirical, model independent method (no templates used). For light curve simulations usually the SALT2 code (Guy et al., 2007, 2010) is applied.

Photometric redshifts derived from multi-band photometry are also proposed for thousands of SNe Ia expected from the Dark Energy Survey (Bernstein et al., 2012), although they preferred the photo-z estimates for the host galaxies rather than the SNe, because the co-added frames of galaxies can be mag deeper than individual SN frames. Sánchez et al. (2014) presented an in-depth comparison of various photo-z methods and codes available for galaxies, and estimated a uncertainty in photo-z for a sample of galaxies.

We propose the photo-z determination for SNe Ia detected with JWST NIRCam by fitting the 4-band SEDs with the Hsiao-templates. This method works for SNe Ia between redshifts, and some examples for the fits to the simulated SN sample are shown in Figure 7. Here the flux uncertainties are derived from the wavelength-dependent flux sensitivity limits for JWST NIRCam as shown on the JWST website7. The best-fit Hsiao-templates are found by simple minimization, which seems to be an adequate solution as long as the Hsiao-templates can indeed model the evolution of rest-frame SEDs of high-redshift SNe Ia in a similar way as their low-redshift counterparts. Note that since the observed NIR fluxes of SNe Ia above are increasingly dominated by their rest-frame optical SEDs, the uncertainties in the rest-frame NIR SEDs do not bias strongly the photo-z determination, especially for events when the peak of the SED shifts into the NIRCam bands (see the lower panels in Figure 7).

Figure 8 (left panel) compares the photo-z estimates with the “true” redshifts for the simulated SN sample. It is seen that the photo-z estimates are the best between the redshift interval, as explained above. For most of the photo-z values are in reasonable agreement with the true redshifts, although there are some deviating SNe having residuals. The overall uncertainty, estimated as the standard deviation of the residuals, is .

It is emphasized that this accuracy can be reached only when the SN is successfully detected in all 4 NIRCam bands. Non-detection in any of these bands can degrade the quality of the fitting, thus, the accuracy of the photo-z estimate.

The right panel of Figure 8 plots the residuals between the simulated and recovered rest-frame phases (i.e. rest-frame days from epoch of maximum light) against redshift. The phases of all the simulated observations could be recovered within days, most of them within days. Again, the phase determination seems to work better for SNe. The uncertainty of the phase determination, estimated as above, is found to be days.

It is concluded that in the redshift interval accurate flux measurements of SNe Ia with 4 JWST NIRCam filter bands allow redshift and phase estimates with and day uncertainties, respectively. Note again that since dust extinction within the host galaxies is ignored in this simulation, similar to other disturbing circumstances like e.g. the host galaxy contamination in the simulated SN fluxes, our results are somewhat optimistic, but may serve as a guideline to what can be expected in an ideal case.

6.3 Color-color diagrams

Figure 9: F200WF444W vs F150WF356W color indices of Type Ia SNe. The points corresponding to the same rest-frame epochs (, 15, 20 or 25 rest-frame days after explosion, as indicated in the legend) but different redshifts (between ) are connected with a colored curve.
Figure 10: The redshift dependence of the F200WF444W color (left panel) and F105WF356W (right panel). The colored curves correspond to the same rest-frame epochs as in Figure 9.

Tanaka et al. (2013) showed that a near-IR color-color diagram can be a useful tool to identify SLSNe and separate them from fainter foreground transients, like Type II-P SNe that have similar light variation timescales. They proposed the usage of F200W, F227W and F356W filters in the following combinations: F200WF277W versus F277WF356W ([2.0][2.8] and [2.8][3.6] in their notation). They concluded that faint objects that have positive colors ( magnitude) in both of these combinations are likely to be high-redshift SLSNe.

In the FLARE project Wang et al. (2017) proposed the application of the F200W vs. F200WF444W color-magnitude diagram for classifying various types of transients to be discovered with JWST NIRCam. They confirmed that SLSNe indeed occupy a different region than SNe Type Ia or Type II, although they noted that “ambiguities are inevitable and more data are needed”.

Since the classification problem of SLSNe based on JWST colors seems to be solved, we concentrate on identifying SNe Ia using the NIRCam filters. After examining various combinations of the 4 NIRCam filters considered in this paper (F150W, F200W, F356W and F444W, see Section 2), we suggest the following combination: F150WF356W and F200WF444W. A color-color plot with these indices is shown in Figure 9. Each colored curve corresponds to the same rest-frame epoch after explosion (as indicated in the legend) but different redshifts between .

In Figure 10 the redshift dependence of these color indices are plotted. In Figure 9 the curves occupy the same narrow diagonal region for each epoch, which suggests that SNe Ia observed within week around peak in rest-frame days are likely to be found in this region (at least if dust extinction in the host galaxy is negligible). Although it requires successful detection of the SN in all proposed NIRCam bands, such a color-color plot can be useful for separating Type Ia SNe from other transients within the same FoV.

6.4 The Hubble-diagram

Figure 11: Hubble-diagrams of simulated SNe. Left panel: the “observed” peak magnitudes in the 4 NIRCam bands (color-coded as indicated in the legend) against redshift. Right-panel: the K-corrected V-band magnitudes of the simulated SNe (black circles), the recovered V-band magnitudes from template fitting (green squares) and the same data but after correcting for the distribution of the peak brightness as determined from template fitting (red dots).

The left panel in Figure 11 contains the “observed” Hubble-diagram, i.e. the AB-magnitudes of the simulated SNe that passed the detection criterion as functions of redshift, in the 4 NIRCam bands. As expected, the scatter on this uncorrected Hubble-diagram exceeds 1 mag in all bands above due to i) the random sampling of the light curve in the observer’s frame, ii) the intrinsic dispersion in the peak magnitudes of SNe Ia (cf. Figure 6) and iii) K-corrections due to non-negligible redshifts.

The current state-of-the-art for correcting for all these effects in order to get a “clean” Hubble-diagram from SN observations is the application of one of the light curve fitting methods (usually SALT2, see e.g. Scolnic et al., 2018). In the present case, however, such an approach does not work, as none of the SNe are detected more than twice due to the relatively long adopted cadence (90 days). Thus, alternatives are needed.

Since the only source of information is the flux in different bands (i.e. the SED of the SN), the peak absolute magnitude of the detected SNe must be determined somehow from their measured SED. This is actually done when measuring the photo-z of the SNe (Section 6.2): an output parameter of that fitting is the K-corrected V-band peak absolute magnitude of the best-fit Hsiao-template to a particular SN. In the right panel of Figure 11 this quantity is plotted against redshift for all simulated SNe (taken from the input database of the simulation; black circles) as well as their recovered values after template fitting (green squares). The red dots show the ideal case, when the correction for the intrinsic distribution of the peak magnitudes (assumed as a Gaussian, Section 6) can also be made. This last step would require the knowledge of not only the fiducial peak magnitude of SNe Ia, but also the underlying distribution of the peak magnitudes as a function of redshift, which may not be Gaussian for high- SNe. Thus, the impressively low scatter of the red dots in the right panel may not be reached from real data without obtaining short-cadence light curves. But even if it were not feasible with JWST due to observability and budget limits, the reduced scatter of the green squares compared to the mag scatter in the left panel of Figure 11 is encouraging.

The green data in the right panel in this Figure reveals another effect that may bias the distribution of the measurements on this kind of Hubble-diagram: at only the SNe that are intrinsically brighter than the mean of their peak brightness distribution are detected. As the red dots suggest, this Malmquist-bias were clearly not present if the correction for the underlying distribution could be made. Nevertheless, this effect must be taken into account when the Hubble-diagram from such high- SN observations are to be tested with cosmological models.

The results above suggests that using such low-cadence JWST data of SNe Ia for cosmology is not trivial, and more thorough studies, which are beyond the scope of the present paper, are necessary to reach this ambitious goal.

7 Summary

The results presented in this paper are summarized as follows.

The 90-day cadence survey for transients in the JWST CVZ, as proposed by the FLARE project (Wang et al., 2017), is shown to be capable of discovering 5 - 20 SLSNe (depending on the metallicity dependence of their rates), as well as SNe Ia between the redshift interval during the 3 year-long survey.

Although SLSNe could be detected at , their low rates probably prevent the discovery of such events above . On the other hand, SNe Ia discovered at may be able to constrain their progenitor scenarios (both the SD and the DD channels) and the fraction of prompt Ia population better than the currently available data.

From simulated observations of high-redshift SNe Ia with JWST NIRCam filters we propose the usage of the F200WF444W vs. F150WF356W color-color diagram to select potential SNe Ia from the observations. These color indices show only weak dependence on the rest-frame phase of the SN around peak, and may also be useful in getting rough estimates for the redshift.

We show that photometric redshifts can be obtained purely from measuring accurate fluxes in these four JWST NIRCam bands by fitting the observations with the Hsiao-templates. The accuracy of these photo-z estimates () depends weakly on redshift, even though the method works better for SNe when the peak of the SED is redshifted into the region of the NIRCam bands. Similarly, the accuracy of the SN epochs recovered from SED-fitting is days.

The same SED-fitting may also be used to get estimates on the K-corrected peak absolute magnitude of the observed SNe in the V-band, provided the Hsiao-templates indeed represent the high- SNe as well as their low- counterparts. At least this correction is necessary to extend the Hubble-diagram to . The resulting data will be still affected by the Malmquist-bias. In order to correct for such effects one would probably need lower cadence light curves with JWST, and more thorough studies are necessary before using these high-redshift SNe Ia observations for cosmology.

This work has been supported by the project ”Transient Astrophysical Objects” GINOP 2.3.2-15-2016-00033 of the National Research, Development and Innovation Office (NKFIH), Hungary, funded by the European Union. We are indebted to Lifan Wang, Jeremy Mould, J. Craig Wheeler, Avishay Gal-Yam, Peter Brown and all other members of the FLARE Collaboration for many hours of enlightening discussion on discovering the high-redshift Universe with JWST during the preparatory work of the FLARE project. \facilitiesJWST \softwareastropy (Astropy Collaboration, 2013), sncosmo (Barbary et al., 2016)

Footnotes

  1. journal: ApJ
  2. without metallicity correction
  3. with metallicity correction
  4. without metallicity correction
  5. with metallicity correction
  6. http://sncosmo.readthedocs.io/en/v1.6.x/
  7. https://jwst-docs.stsci.edu/display/JTI/NIRCam+Sensitivity

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